Galatians 4:23 But he who was of the bondwoman was born after the flesh; but he of the freewoman was by promise.
The son of the bondwoman was born after the Flesh. Key to understanding the two covenants, the one born according to the flesh, or by mans desire. we know that The Gospel of John say . But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name: Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God (John 1; 12,13) no one can be justified in the flesh. So we see through the example of Ishmael who was born of the flesh and that represented the first covenant in that he being born of a bondwoman.
Was born after the flesh; after the common order and course of nature, through the copulation of two persons, the one able to procreate, and the other fit for the conception of children; and was typical of the Jews, the natural descendants of Abraham, who, as such, and upon that account, were not the children of God, nor heirs of the eternal inheritance (John Gill)
The son of the free woman was born through the promise, by Sarah who had passed the age. This was a promise from God to Abraham that he would be the father of many nations. A prophecy that is now being fulfilled. Paul was debating scripture with scripture, for those who wanted to stay with the old covenant or try to intertwine them, that the bondwoman and the free woman are two separate covenants. One law and bondage the other the promise and Grace. One by the will of the flesh the other by the will of God.